Chapter 9 Sinusoids and Phasors Deltatowye and wyetodelta

Chapter 9 Sinusoids and Phasors Ø Delta-to-wye and wye-to-delta conversions Ø Phase Sifters. Ø

Y-Δ and Δ-Y Equivalent Circuits Ø Y-Δ and Δ-Y type equivalent conversions will be

Balanced Y-Δ and Δ-Y Equivalent Circuits Ø A delta (Δ) or Y (wye) circuit

Find I in the circuit given? Converting Δ Connection to Y form, we obtain

Phase Shifters (Leading Output) Ø Phase shifting is employed to correct undesirable phase shift

Phase Shifters (Lagging Output) Ø Phase shifting is employed to correct undesirable phase shift

P. P. 9. 13 Design an RC circuit that provide 90° lagging phase shift.

AC Bridges Ø The AC bridge is Balanced when no current flows through the

AC Bridges Ø Unknown capacitance and inductances Cx and Lx are measured in terms

Ch 9, Prob 55. Find Z in the network given that Eeng 224 16

Chapter 9, Problem 77 a) Calculate the phase shift at 2 Mhz. b) Calculate

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Chapter 9 Sinusoids and Phasors Ø Delta-to-wye and wye-to-delta conversions Ø Phase Sifters. Ø AC Bridges. Ø Problem Solutions Huseyin Bilgekul Eeng 224 Circuit Theory II Department of Electrical and Electronic Engineering Eastern Mediterranean University Eeng 224 1

Y-Δ and Δ-Y Equivalent Circuits Ø Y-Δ and Δ-Y type equivalent conversions will be most useful when considering Three Phase circuits. Ø Impedances Z 1, Z 2 and Z 3 are Y connected. Ø Impedances Za, Zb and Zc are Δ connected. Ø Y and Δ forms can be eqivalently converted from one form to the other. Ø Y-Δ and Δ-Y conversions are valid for impedances as well as resistive circuits. Eeng 224 2

Y-Δ and Δ-Y Equivalent Circuits Ø Y-Δ and Δ-Y type equivalent conversions will be useful when considering Three Phase circuits in Chapter 12. Eeng 224 3

Balanced Y-Δ and Δ-Y Equivalent Circuits Ø A delta (Δ) or Y (wye) circuit is balanced if it has equal impedances in all three branches. Ø Y-Δ and Δ-Y conversions is very simple for balanced circuits. Eeng 224 4

Find I in the circuit given? Converting Δ Connection to Y form, we obtain Converting to Y form, we can simplify the circuit by combining the parallel and series elements Z Eeng 224 5

P. P. 9. 12 Continued Eeng 224 6

Phase Shifters (Leading Output) Ø Phase shifting is employed to correct undesirable phase shift of the AC voltage. Leading Output Leads the input Eeng 224 7

Phase Shifters (Lagging Output) Ø Phase shifting is employed to correct undesirable phase shift of the AC voltage. Lagging Output Lags the input Eeng 224 8

P. P. 9. 13 Design an RC circuit that provide 90° lagging phase shift. Find the output voltage if 10 Volt is applied. Eeng 224 9

Eeng 224 10

AC Bridges Ø The AC bridge is Balanced when no current flows through the meter. AC bridges are used in measuring inductance and capacitance values. A general AC bridge circuit Eeng 224 11

AC Bridges Ø Unknown capacitance and inductances Cx and Lx are measured in terms of the known standard values Cs and Ls AC Bridge for measuring L AC Bridge for measuring C. Eeng 224 12

Eeng 224 13

Chapter 9, Problem 41. Eeng 224 14

Chapter 9, Problem 51. Eeng 224 15

Ch 9, Prob 55. Find Z in the network given that Eeng 224 16

Chapter 9, Problem 77 a) Calculate the phase shift at 2 Mhz. b) Calculate the frequency at which phase shift is 45 degree. Eeng 224 17

Chapter 9, Problem 77 a) Calculate the phase shift at 2 Mhz. b) Calculate the frequency at which phase shift is 45 degree. Eeng 224 18